Find the Center, Transverse Axis, Vertices, Foci, and Asymptotes of the Hyperbola

question 36

Multiple Choice

Find the center, transverse axis, vertices, foci, and asymptotes of the hyperbola.
- $$( x - 1 ) ^ { 2 } - 4 ( y - 2 ) ^ { 2 } = 4$$

• A) center at \(( 1,2 )\)
• transverse axis is parallel to \(\mathrm { y }\)-axis
• vertices at \(( 1,0 )\) and \(( 1,4 )\),
• foci at \(( 1,2 - \sqrt { 5 } )\) and \(( 1,2 + \sqrt { 5 } )\),
• asymptotes of \(y + 2 = - 2 ( x + 1 )\) and \(y + 2 = 2 ( x + 1 )\)
• B) center at \(( 1,2 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( 0,2 )\) and \(( 2,2 )\)
• foci at \(( 1 - \sqrt { 5 } , 2 )\) and \(( 1 + \sqrt { 5 } , 2 )\)
• asymptotes of \(y - 2 = - 2 ( x - 1 )\) and \(y - 2 = 2 ( x - 1 )\)
• C) center at \(( 1,2 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( - 1,2 )\) and \(( 3,2 )\)
• foci at \(( 1 - \sqrt { 5 } , 2 )\) and \(( 1 + \sqrt { 5 } , 2 )\)
• asymptotes of \(y - 2 = - \frac { 1 } { 2 } ( x - 1 )\) and \(y - 2 = \frac { 1 } { 2 } ( x - 1 )\)
• D) center at \(( 2,1 )\)
• transverse axis is parallel to \(x\)-axis
• vertices at \(( 0,1 )\) and \(( 4,1 )\)
• foci at \(( 2 - \sqrt { 5 } , 1 )\) and \(( 2 + \sqrt { 5 } , 1 )\)
• asymptotes of \(y - 1 = - \frac { 1 } { 2 } ( x - 2 )\) and \(y - 1 = \frac { 1 } { 2 } ( x - 2 )\)

Understand the basic principles and characteristics of AC and DC circuits, including waveform analysis.

Identify and explain the key electrical properties such as resistance, capacitive, and inductive loads.

Understand the concept of rectification and its effects on AC signals moving to DC.

Calculate and differentiate between peak, RMS, peak-to-peak, and average values in AC circuits.

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